IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/36460.html
   My bibliography  Save this paper

Validity and precision of estimates in the classical newsvendor model with exponential and rayleigh demand

Author

Listed:
  • Halkos, George
  • Kevork, Ilias

Abstract

In this paper we consider the classical newsvendor model with profit maximization. When demand is fully observed in each period and follows either the Rayleigh or the exponential distribution, appropriate estimators for the optimal order quantity and the maximum expected profit are established and their distributions are derived. Measuring validity and precision of the corresponding generated confidence intervals by respectively the actual confidence level and the expected half-length divided by the true quantity (optimal order quantity or maximum expected profit), we prove that the intervals are characterized by a very important and useful property. Either referring to confidence intervals for the optimal order quantity or the maximum expected profit, measurements for validity and precision take on exactly the same values. Furthermore, validity and precision do not depend upon the values assigned to the revenue and cost parameters of the model. To offer, therefore, a-priori knowledge for levels of precision and validity, values for the two statistical criteria, that is, the actual confidence level and the relative expected half-length are provided for different combinations of sample size and nominal confidence levels 90%, 95% and 99%. The values for the two criteria have been estimated by developing appropriate Monte-Carlo simulations. For the relative-expected half-length, values are computed also analytically.

Suggested Citation

  • Halkos, George & Kevork, Ilias, 2012. "Validity and precision of estimates in the classical newsvendor model with exponential and rayleigh demand," MPRA Paper 36460, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:36460
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/36460/1/MPRA_paper_36460.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Khouja, Moutaz, 1999. "The single-period (news-vendor) problem: literature review and suggestions for future research," Omega, Elsevier, vol. 27(5), pages 537-553, October.
    2. Jammernegg, Werner & Kischka, Peter, 2009. "Risk preferences and robust inventory decisions," International Journal of Production Economics, Elsevier, vol. 118(1), pages 269-274, March.
    3. Marcelo Olivares & Christian Terwiesch & Lydia Cassorla, 2008. "Structural Estimation of the Newsvendor Model: An Application to Reserving Operating Room Time," Management Science, INFORMS, vol. 54(1), pages 41-55, January.
    4. Grubbström, Robert W., 2010. "The Newsboy problem when customer demand is a compound renewal process," European Journal of Operational Research, Elsevier, vol. 203(1), pages 134-142, May.
    5. Su, Rung Hung & Pearn, Wen Lea, 2011. "Product selection for newsboy-type products with normal demands and unequal costs," International Journal of Production Economics, Elsevier, vol. 132(2), pages 214-222, August.
    6. Kevork, Ilias S., 2010. "Estimating the optimal order quantity and the maximum expected profit for single-period inventory decisions," Omega, Elsevier, vol. 38(3-4), pages 218-227, June.
    7. Casimir, Rommert J., 2002. "The value of information in the multi-item newsboy problem," Omega, Elsevier, vol. 30(1), pages 45-50, February.
    8. Wang, Charles X. & Webster, Scott, 2009. "The loss-averse newsvendor problem," Omega, Elsevier, vol. 37(1), pages 93-105, February.
    9. Maurice E. Schweitzer & Gérard P. Cachon, 2000. "Decision Bias in the Newsvendor Problem with a Known Demand Distribution: Experimental Evidence," Management Science, INFORMS, vol. 46(3), pages 404-420, March.
    10. Huang, Di & Zhou, Hong & Zhao, Qiu-Hong, 2011. "A competitive multiple-product newsboy problem with partial product substitution," Omega, Elsevier, vol. 39(3), pages 302-312, June.
    11. Jorge Ibarra-Salazar, 2005. "The Newsboy Model: Changes in Risk and Price," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 30(1), pages 99-109, June.
    12. Chen, Liang-Hsuan & Chen, Ying-Che, 2010. "A multiple-item budget-constraint newsboy problem with a reservation policy," Omega, Elsevier, vol. 38(6), pages 431-439, December.
    13. Matsuyama, Keisuke, 2006. "The multi-period newsboy problem," European Journal of Operational Research, Elsevier, vol. 171(1), pages 170-188, May.
    14. Lee, Chih-Ming & Hsu, Shu-Lu, 2011. "The effect of advertising on the distribution-free newsboy problem," International Journal of Production Economics, Elsevier, vol. 129(1), pages 217-224, January.
    15. Hill, Roger M., 1997. "Applying Bayesian methodology with a uniform prior to the single period inventory model," European Journal of Operational Research, Elsevier, vol. 98(3), pages 555-562, May.
    16. Hon-Shiang Lau, 1997. "Simple formulas for the expected costs in the newsboy problem: An educational note," European Journal of Operational Research, Elsevier, vol. 100(3), pages 557-561, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Halkos, George & Kevork, Ilias, 2012. "Evaluating alternative frequentist inferential approaches for optimal order quantities in the newsvendor model under exponential demand," MPRA Paper 39650, University Library of Munich, Germany.
    2. Halkos, George & Kevork, Ilias, 2012. "Unbiased estimation of maximum expected profits in the Newsvendor Model: a case study analysis," MPRA Paper 40724, University Library of Munich, Germany.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Halkos, George & Kevork, Ilias, 2012. "Evaluating alternative estimators for optimal order quantities in the newsvendor model with skewed demand," MPRA Paper 36205, University Library of Munich, Germany.
    2. Huang, Di & Zhou, Hong & Zhao, Qiu-Hong, 2011. "A competitive multiple-product newsboy problem with partial product substitution," Omega, Elsevier, vol. 39(3), pages 302-312, June.
    3. Kevork, Ilias S., 2010. "Estimating the optimal order quantity and the maximum expected profit for single-period inventory decisions," Omega, Elsevier, vol. 38(3-4), pages 218-227, June.
    4. Halkos, George & Kevork, Ilias, 2012. "Evaluating alternative frequentist inferential approaches for optimal order quantities in the newsvendor model under exponential demand," MPRA Paper 39650, University Library of Munich, Germany.
    5. Halkos, George & Kevork, Ilias, 2011. "Non-negative demand in newsvendor models:The case of singly truncated normal samples," MPRA Paper 31842, University Library of Munich, Germany.
    6. Banerjee, Pradeep K. & Turner, T. Rolf, 2012. "A flexible model for the pricing of perishable assets," Omega, Elsevier, vol. 40(5), pages 533-540.
    7. Khanra, Avijit & Soman, Chetan & Bandyopadhyay, Tathagata, 2014. "Sensitivity analysis of the newsvendor model," European Journal of Operational Research, Elsevier, vol. 239(2), pages 403-412.
    8. Halkos, George & Kevork, Ilias, 2012. "The classical newsvendor model under normal demand with large coefficients of variation," MPRA Paper 40414, University Library of Munich, Germany.
    9. Khanra, Avijit & Soman, Chetan, 2013. "Sensitivity Analysis of the Newsboy Model," IIMA Working Papers WP2013-09-03, Indian Institute of Management Ahmedabad, Research and Publication Department.
    10. Halkos, George & Kevork, Ilias, 2012. "Unbiased estimation of maximum expected profits in the Newsvendor Model: a case study analysis," MPRA Paper 40724, University Library of Munich, Germany.
    11. Marziyeh Karimi & Amir Hossein Niknamfar & Seyed Hamid Reza Pasandideh, 2017. "Two-stage single period inventory management for a manufacturing vendor under green-supplier supply chain," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(4), pages 704-718, December.
    12. Chung‐Yee Lee & Xi Li & Mingzhu Yu, 2015. "The loss‐averse newsvendor problem with supply options," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(1), pages 46-59, February.
    13. Shen, Houcai & Pang, Zhan & Cheng, T.C.E., 2011. "The component procurement problem for the loss-averse manufacturer with spot purchase," International Journal of Production Economics, Elsevier, vol. 132(1), pages 146-153, July.
    14. Wang, Charles X., 2010. "The loss-averse newsvendor game," International Journal of Production Economics, Elsevier, vol. 124(2), pages 448-452, April.
    15. Arcelus, F.J. & Kumar, Satyendra & Srinivasan, G., 2012. "Risk tolerance and a retailer's pricing and ordering policies within a newsvendor framework," Omega, Elsevier, vol. 40(2), pages 188-198, April.
    16. Shaofu Du & Yujiao Zhu & Tengfei Nie & Haisuo Yu, 2018. "Loss-averse preferences in a two-echelon supply chain with yield risk and demand uncertainty," Operational Research, Springer, vol. 18(2), pages 361-388, July.
    17. Zhang, Xiang, 2014. "Reference-dependent electric vehicle production strategy considering subsidies and consumer trade-offs," Energy Policy, Elsevier, vol. 67(C), pages 422-430.
    18. Jörnsten, Kurt & Lise Nonås, Sigrid & Sandal, Leif & Ubøe, Jan, 2012. "Transfer of risk in the newsvendor model with discrete demand," Omega, Elsevier, vol. 40(3), pages 404-414.
    19. Sévi, Benoît, 2010. "The newsvendor problem under multiplicative background risk," European Journal of Operational Research, Elsevier, vol. 200(3), pages 918-923, February.
    20. Guo, Peijun & Ma, Xiuyan, 2014. "Newsvendor models for innovative products with one-shot decision theory," European Journal of Operational Research, Elsevier, vol. 239(2), pages 523-536.

    More about this item

    Keywords

    Inventory Control; Classical newsvendor model; Exponential and Rayleigh Distributions; Confidence Intervals; Monte-Carlo Simulations;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:36460. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.